Technical Field
The embodiments herein generally relate to voltage follower, and more particularly, to a circuit and method for maximizing the gain of the voltage follower.
Description of the Related Art
Voltage followers, also known as a unity gain buffers, are commonly used circuits in many designs. Typically, an output of a voltage follower follows or tracks an input voltage. Voltage follower circuits typically have high input impedance and low output impedance. One of the common applications of voltage follower circuits is in the design of multistage filters. Voltage followers are used in design of multistage filters to isolate each stage of the multistage filter from the other. Another application of the voltage follower is to drive Analog to Digital (ADC) convertors. The advantage of using voltage followers for this application is that, in some cases ADCs can sample inputs having large current and it is very important to control the current at each stage.
Also, voltage followers can behave as voltage buffers. For instance, if the output resistance of a first stage of a design is high, it is recommended to add a voltage follower at its output to function as a voltage buffer, so that the voltage in the next and later stages will almost be the same as it is in the first stage.
FIG. 1 illustrates a conventional voltage follower circuit 100 according to an exemplary scenario. The conventional voltage follower circuit 100 includes an n-channel metal oxide semi-conductor (NMOS) transistor 102, an input voltage Vin 104, an output voltage Vout 106, a fixed voltage 108, and a ground terminal 110. The NMOS transistor 102 includes a gate terminal 112, a drain terminal 114, and a source terminal 116. The input voltage Vin 104 is provided as an input at the gate terminal 112 and the output voltage Vout 106 is obtained as an output at the source terminal 116. The fixed voltage 108 is connected to the drain terminal 114. In one embodiment, the source terminal 116 is connected to a bias current source, and other terminal of the bias current source is connected to the ground terminal 110.
FIG. 2 illustrates a small signal model of the conventional voltage follower circuit 200 according to an exemplary scenario. The small signal model of the conventional voltage follower circuit 200 includes an input voltage Vin 104, an output voltage Vout 106, a ground terminal 110, and a voltage controlled current source 202. In an embodiment, the current source 202 models the transconductance gm of the NMOS transistor 102, and r0 is used to model the output resistance of the transistor. The transconductance gm is a ratio of the current variation at the output to the voltage variation between the gate terminal 112 and the source terminal 116. The transconductance is also known as mutual conductance. In an embodiment, a small signal model also known as AC analysis model is used for calculation of the gain. The relation is as follows:gm*(Vin−Vout)*r0=Vout
However Gain (G)=Vout/Vin.
Hence, Gain (G)=gm*r0/(1+gm*r0);
and the effective input capacitance (Cin) of the circuit 200 is given by the equation,Cin=Cgd+Cgs(1−(gm*r0)/(1+gm*r0))=Cgd+Cgs(1−G)
where,
Cin is the total input capacitance.
Cgd is the measure of capacitance between the gate terminal 112 and drain terminal 116 of the NMOS transistor 102. Cgs is the measure of the capacitance between the gate terminal 112 and source terminal 116 of the NMOS transistor. In one embodiment, assuming reasonable values for gm*r0, Cgd and Cgs (i.e. gm*r0=˜10), an approximate value of gain may be 10/11=0.909. In one embodiment, if the Cgd=C, then Cgs=˜2*C, and so Cin=˜1.182*C.
The gain of the ideal voltage follower is equal to 1. Because of the finite output impedance of the transistor (r0), the gain of the conventional voltage follower is approximately 0.909. By increasing the value of gm*r0, the gain of the conventional voltage follower circuit 100 can be brought closer to 1. In one embodiment, the gain of the conventional voltage follower circuit 100 is increased by increasing both W and L proportionally while maintaining the same W/L, but the input capacitance (Cin) is increased significantly since all the capacitances (Cgd and Cgs) are functions of W*L. Consequently, the input impedance of the voltage follower is reduced at higher frequencies making it difficult to drive it. Therefore, it is also advantageous to keep the input capacitance of the voltage follower as low as possible.
Accordingly, there remains a need for a circuit and a method to maximize the gain of the voltage follower circuit in an efficient way.